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Required information Exercise 5A-2 (Algo) Least-Squares Regression [LO5-11] [The following information applies to the questions displayed below.] Bargain Rental...

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Accounting

Required information

Exercise 5A-2 (Algo) Least-Squares Regression [LO5-11]

[The following information applies to the questionsdisplayed below.]

Bargain Rental Car offers rental cars in an off-airport locationnear a major tourist destination in California. Management wouldlike to better understand the variable and fixed portions of itscar washing costs. The company operates its own car wash facilityin which each rental car that is returned is thoroughly cleanedbefore being released for rental to another customer. Managementbelieves that the variable portion of its car washing costs relatesto the number of rental returns. Accordingly, the following datahave been compiled:

MonthRental ReturnsCar Wash Costs
January2,500$12,000
February2,500$13,600
March2,800$12,800
April3,200$15,800
May3,700$17,200
June5,200$25,300
July5,600$23,200
August5,700$24,700
September4,800$23,800
October4,700$24,100
November2,300$11,700
December3,200$17,700

Exercise 5A-2 Part 2 (Algo)

2. Using least-squares regression, estimate the variable costper rental return and the monthly fixed cost incurred to wash cars.(Round Fixed cost to the nearest whole dollar amount andthe Variable cost per unit to 2 decimal places.)

Answer & Explanation Solved by verified expert
4.1 Ratings (844 Votes)

Month x=rental returns y = car wash costs xy X2
Jan 2,500 12,000 3,00,00,000 62,50,000
Feb 2,500 13,600 3,40,00,000 62,50,000
Mar 2800 12,800 3,58,40,000 78,40,000
April 3200 15,800 5,05,60,000 1,02,40,000
May 3700 17,200 6,36,40,000 1,36,90,000
June 5200 25,300 13,15,60,000 2,70,40,000
July 5600 23,200 12,99,20,000 3,13,60,000
Aug 5700 24,700 14,07,90,000 3,24,90,000
Sep 4800 23,800 11,42,40,000 2,30,40,000
Oct 4700 24,100 11,32,70,000 2,20,90,000
Nov 2300 11,700 2,69,10,000 52,90,000
Dec 3200 17,700 5,66,40,000 1,02,40,000
Total 46,200 2,21,900 92,73,70,000 19,58,20,000

N = number of months = 12

Variable cost per rental return =( N ?xy ? ?x ?y)/{(N ?x²) ? (?x)²}

Variable cost per rental return ={( 12 × 92,73,70,000) - (46,200× 2,21,900) } / {(12 ×19,58,20,000) - (46,200)²}

On solving VC per Rental return = 4.0699 or 4.07

Fixed Cost per month = {?y - ( Variable cost per rental return × ?x )/N

Fixed Cost per month = {2,21,900 - (4.07 × 46,200)} /12

Fixed cost Per month = 33,866/12 = 2822.17
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